Authors:

Wei-Tao Bi(Peking University)

Bin Wu(Peking University)

Zhen-Su She(Peking University)

Fazle Hussain(Texas Tech University)

A symmetry based approach is applied to analyze the mean velocity and
temperature fields of compressible, flat plate turbulent boundary layers
(CTBL). A Reynolds stress length scale and a turbulent heat flux length
scale are identified to possess the same defect scaling law in the CTBL
bulk, which is solely owing to the constraint of the wall to the geometry of
the wall-attached eddies, but invariant to compressibility and wall heat
transfer. This invariance is called the geometric invariance of CTBL eddies
and is likely the origin of the Mach number invariance of Morkovin's
hypothesis, as well as the similarity of energy and momentum transports. A
closure for the turbulent transport by using the invariant lengths is
attainted to predict the mean velocity and temperature profiles in the CTBL
bulk- superior to the van Driest transformation and the Reynolds analogy
based relations for its sound physics and higher accuracy. Additionally, our
approach offers a new understanding of turbulent Prandtl number.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2015.DFD.L21.6